That sounds a lot like an ISP,

No, that sounds exactly like Nostr, which is a lot more practical and cheap to run that a Mastodon server and actually scales quite well.

moving all your storage to the edge is usually a bad idea.

No. You just need to move the application state to the edge. Storage itself can still be in content-addressable data servers, like IPFS, magnet links or plain-old (S)FTP servers.

When someone posts a picture on Mastodon, the picture itself is not replicated, just a link to it. Now, imagine that your "smart client" version of Mastodon (or Peertube, or Lemmy) wants to post a picture. How would it work?

• User posts the photo to an IPFS server. It could be a cloud server or it could be their own NAS they have it running at home.
• The uploaded photo generates a hash.
• Client takes the hash of the photo and puts in the message.
• Client signs a message and send to the server
• Server receives the message, processes it (index metadata, puts the image in its cache to help with seeding, etc)
• The server has a policy of keeping the image in the cache in the outbox until it has been delivered to at least 70% of the other clients or 5 days, whichever happens first.

I think that servers are needed.

If by "servers" you mean "nodes in the network that are more stable and have stronger uptime/performance guarantees", I agree 100%. If by "servers" you mean "centralized nodes responsible for application logic" then I'd say you can be easily be proven wrong by actual examples of distributed apps.